Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

A study of a country\'s colleges and universities resulted in the demand equatio

ID: 3311436 • Letter: A

Question

A study of a country's colleges and universities resulted in the demand equation q = 20,000 2p, where q is the enrollment at a public college or university and p is the average annual tuition (plus fees) it charges.† Officials at Enormous State University have developed a policy whereby the number of students it will accept per year at a tuition level of p dollars is given by q = 9,100 + 0.5p. Find the equilibrium tuition price p and the consumers' and producers' surpluses at this tuition level. What is the total social gain at the equilibrium price? HINT [See Example 3.] equilibrium tuition price p = $ consumers' surplus CS = $ producers' surplus PS = $ total social gain $

Explanation / Answer

Equilibrium tuition price= 4600

Social gain= 10800

Explanation:

20,000-2p=9100+0.5p

Collecting the like terms,

2.5p=10900

Therefore, p=4600 Hence, the equilibrium tuition price=4600

The social gain is in terms of student enrollment, thus q=20000-2*4600=10800 students

q=9500+0.5*4600=11800 students